Final answer:
The correct equation for a line perpendicular to y = (2/9)x + 1 is 9x - 2y = 1, since it has a slope that is the negative reciprocal of 2/9, which is -9/2.
Step-by-step explanation:
The student is asking for the equation of a line that is perpendicular to the line represented by y = (2/9)x + 1. The slope of the given line is 2/9. For a line to be perpendicular to this one, its slope must be the negative reciprocal of 2/9, which is -9/2. This means the slope of the required line is -9/2. Of the options provided, the correct equation that has a slope of -9/2 is 9x - 2y = 1, which can be rewritten in slope-intercept form as y = (9/2)x - (1/2) to confirm its slope. Therefore, the answer to the question is d) 9x - 2y = 1.